基于项目反应理论和量子智能算法的选题策略研究

发布时间：2018-06-24 21:06

本文选题：选题策略 + 普通遗传算法　；参考：《南京师范大学》2014年博士论文

【摘要】：为了对量子智能算法用于测验选题的可行性和特性进行探索,本文将普通遗传算法和量子遗传算法、普通粒子群算法和量子粒子群算法、普通蚁群算法和量子蚁群算法的选题性能进行两两比较。本研究是基于模拟题库的研究,采用项目反应理论的三参数逻辑斯蒂模型建立各算法的目标函数,各算法得到的选题结果采用方差分析进行差异显著性检验,分析影响选题结果的参数、得到算法的最优参数组合。在三对算法中选出较优的三种算法再进行比较,得到本实验最优的选题算法。研究结果充实了当前的选题策略理论,并首次成功将量子智能算法用于选题。方法论上,不仅在选题领域是个突破,而且还为人工智能在心理测量中的应用扩充了新的内容。主要研究结论有以下几点:(1)遗传算法进行本研究的选题实验的结果表明:虽然分数线处测验信息量比较大,但是多次选题的标准差也越大,算法不稳健。(2)用量子遗传算法的九种参数组合进行选题实验,进行结果分析和讨论后得出:若将分数线处测验信息量指标视为最重要,不考虑平坦度和时间,可选择种群大小80,迭代次数为500。若综合考虑三个指标,信息量要尽量大,平坦度也大,且选题时间短可以选择种群为80,迭代次数为300。(3)采用t检验对普通遗传算法和量子遗传算法的分数线处最大测验信息量、分数线附近信息量平坦度进行分析,结果显示,在同样的种群大小和迭代次数下,普通遗传算法虽然在大部分情况下的最大测验信息函数大于量子遗传算法的。但是,普通遗传算法选题的分数线附近信息量平坦度值显著差于量子遗传算法的。另外,从选题时间、算法的稳健性的角度来看,量子遗传算法的选题时间大大短于普通遗传算法,稳健性大大优于普通遗传算法。因此量子遗传算法用于选题的综合性能优于普通遗传算法。(4)虽然粒子群算法用于解决其它优化问题时,c1和c2取值使得优化结果不同。但是本文首次采用方差分析法进行差异显著性检验,结果显示粒子群算法进行选题时,c1和c2取不同值对分数线处信息量、分数线附近信息量平坦度和选题时间没有显著影响,因此可以在[1,4]之间任意取值。(5)量子粒子群算法选题实验结果表明,惯性权重w1和W2对最大测验信息函数没有显著影响,但是对信息量平坦度有显著影响。因此选题时要考虑其取值,量子粒子群的最佳参数组合有以下两种情况:若是将分数线处测验信息量和信息量平坦度指标视为最重要时:W1的最佳取值为1.2,W2为0.3,粒子数量取40,迭代次数为700。若是综合考虑三个指标的重要性时,W1的最佳取值为1.2,W2为0.3,粒子数量取40,迭代次数为300。(6)采用t检验对两种算法的分数线处最大测验信息量、分数线附近信息量平坦度进行分析,在分数线附近信息量平坦度上,两种算法没有显著差异,但是量子粒子群算法在最大信息量上大部分情况下(5种)显著高于粒子群算法,其选题时间,选题稳健度方面都比粒子群算法略胜一筹,因此,可以认为量子粒子群用于基于项目反应理论的HSK选题时,选题效果要胜出粒子群。(7)量子蚁群算法选题结果表明,若是将分数线处的测验信息量的重要性视为最大,则选择第一种参数组合(ρ=0.1,Q=150, m-70, d=360)。若是综合考虑三个选题指标,则第五种(ρ=0. 5,Q=250,m=50,d=200)参数组合下的选题结果最优。(8)采用t检验对蚁群算法和量子蚁群算法的分数线处最大测验信息量、分数线附近信息量平坦度进行分析,结果显示量子蚁群算法在九种参数条件下,分数线处最大测验信息量显著优于普通蚁群算法,两种算法的信息量平坦度没有显著差异;在算法的稳健性方面,对各算法下选题成卷20次的分数线处最大测验信息量的标准差,试卷的区分度、难度、猜测度的标准差进行分析,结果显示在大部分情况下,量子蚁群算法的稳健性都由于普通蚁群算法。量子蚁群算法明显优于普通蚁群之处是选题时间大大短于蚁群算法。因此,综合考虑各方面的算法评价指标,量子蚁群算法优于普通蚁群算法。(9)对量子遗传、量子粒子群、量子蚁群三种算法用两种方式进行了比较,两种方法的结果都表明,量子遗传算法虽然不是在所有评价指标上都为最优,但是在大部分评价指标上都显示为最优,特别是其选题时间要远远小于其他几种算法,因此量子遗传算法为本次选题的最优算法。
[Abstract]:In order to explore the feasibility and characteristics of quantum intelligent algorithm used to test topic selection, this paper compares the performance of general genetic algorithm and quantum genetic algorithm, ordinary particle swarm algorithm and quantum particle swarm algorithm, common ant colony algorithm and quantum ant colony algorithm. This study is based on the research of analog question bank and adopts the project. The three parameter logistic model of the reaction theory establishes the objective function of each algorithm. The results of each algorithm are tested by variance analysis, analyze the parameters that affect the results of the selected topic, and get the optimal combination of the algorithm. In the three algorithm, three better algorithms are selected to compare, and the optimal experiment is obtained. The research results enrich the current topic selection strategy theory and apply the quantum intelligent algorithm to the topic selection for the first time. Methodology, not only is a breakthrough in the topic selection field, but also expands the new content for the application of artificial intelligence in psychological measurement. The main research results are as follows: (1) genetic algorithm for this study The result of the selected experiment shows that, although the amount of information at the score line is relatively large, the standard deviation of the selected topic is also bigger and the algorithm is not robust. (2) the experiment is carried out with nine parameters combination of quantum genetic algorithm, and the results are analyzed and discussed. And time, the size of the population is 80 and the number of iterations is 500.. If three indexes are taken into consideration, the amount of information should be as large as possible and the degree of flatness is large, and the selection of the selected population is 80 and the number of iterations is 300. (3). The maximum test information at the fractional line at the common genetic algorithm and the quantum genetic algorithm and the letter near the fractional line are used by the t test. The results show that, under the same population size and the number of iterations, the maximum information function of the general genetic algorithm is larger than the quantum genetic algorithm in most cases. However, the level of information level near the score line of the general genetic algorithm is significantly worse than the quantum genetic algorithm. According to the selection time and robustness of the algorithm, the selection time of the quantum genetic algorithm is much shorter than the ordinary genetic algorithm, and the robustness is much better than the ordinary genetic algorithm. Therefore, the comprehensive performance of the quantum genetic algorithm is better than the ordinary genetic algorithm. (4) although the particle swarm optimization algorithm is used to solve other optimization problems, the C1 and C2 values are obtained. The optimization results are different. But the variance analysis method is used for the first time to test the difference saliency. The results show that when the particle swarm optimization is selected, C1 and C2 have no significant influence on the amount of information at the fraction line, the level of information flatness near the fractional line and the selection time, so it can be arbitrarily taken between [1,4]. (5) quantum particles. The experimental results of subgroup algorithm show that the inertia weight W1 and W2 have no significant influence on the maximum test information function, but have significant influence on the flatness of the information quantity. Therefore, the selection of the selected topic should be taken into consideration. The best combination of the quantum particle swarm has the following two cases: if the amount of information and the amount of information at the fraction line is flatness index The best value is 1.2, the best value for W1 is 1.2, the W2 is 0.3, the number of particles is 40, and the number of iterations is 700. if the importance of three indexes is taken into consideration. The best value of the W1 is 1.2, W2 is 0.3, the number of particles is 40, the number of iterations is 300. (6), the maximum test information at the fractional line of the two algorithms and the information near the fractional line are used by t test. There is no significant difference between the two algorithms on the flatness of the amount of information near the fractional line, but the quantum particle swarm algorithm is significantly higher than the particle swarm optimization in most cases (5 kinds) of the maximum information. The time of selection and the robustness of the selected topic are all better than that of the particle swarm optimization. Therefore, the quantum particle can be considered as a quantum particle. When the group is used to select the HSK topic based on the project response theory, the effect of the selected topic is better than the particle swarm. (7) the results of the quantum ant colony algorithm show that the first parameter combination (rho =0.1, Q=150, m-70, d= 360) is selected if the importance of the quantity of test information at the fractional line is considered as the maximum. If the three selection indexes are taken into consideration, the fifth species (P =0. 5) The optimal selection results under the combination of Q=250, m=50 and d=200 are the best. (8) the maximum test information at the score line at the ant colony algorithm and the quantum ant colony algorithm and the flatness of the information quantity near the fractional line are analyzed by using the t test. The results show that the quantum ant colony algorithm is significantly better than the ordinary ant under the nine parameters. In the group algorithm, there is no significant difference in the flatness of the amount of information between the two algorithms; in the robustness of the algorithm, the standard deviation of the maximum test information at the score line of the 20 times under each algorithm, the degree of the test paper, the difficulty and the standard deviation of the guess measure are analyzed. The results show the robustness of the quantum ant colony algorithm in most cases. Because of the common ant colony algorithm, the quantum ant colony algorithm is obviously better than the common ant colony, and the selection time is much shorter than the ant colony algorithm. Therefore, the quantum ant colony algorithm is superior to the common ant colony algorithm considering the evaluation index of all aspects. (9) three algorithms are compared in two ways for quantum genetic, quantum particle swarm and quantum ant colony algorithm, two The results of the method show that, although the quantum genetic algorithm is not the best in all evaluation indexes, it is shown to be the best in most evaluation indexes, especially the selection time of the quantum genetic algorithm is far smaller than that of the other several algorithms, so the quantum genetic algorithm is the best algorithm for this topic.
【学位授予单位】：南京师范大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：B841

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